Integrators for current sensors

ABSTRACT

An integrator for use with a current sensor provides a feedback loop reducing drift while maintaining wide bandwidth.

STATEMENT OF GOVERNMENT INTEREST

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout payment of any royalties thereon or therefor.

FIELD OF THE INVENTION

The invention is related to the field of high bandwidth currentmeasurements, particularly integrators for Rogowski coil currentsensors.

BACKGROUND OF THE INVENTION

Current transducers are critical components in the control andprotection of many devices, including rotating machines. Shuntresistors, current transformers, closed loop Hall Effect, and closedloop fluxgate are some well-known arrangements which are available formaking industrial current measurements. Conventional iron-core currenttransformers (CTs) are usually designed with rated secondary currentsbetween 1-5 A. The ANSI/IEEE standard C57.13-2000 specifies accuracyclasses for both steady state and symmetrical fault conditions. When thefault currents exceed rated current, the CT will saturate resulting indistorted waveforms which have a lower RMS value. CTs have severaldisadvantages, however, particularly in crowded spaces where themechanical structures of CTs are not amenable to measuring differentconductors in such tight locations.

Rogowski coils may overcome certain such disadvantages of CTs, as theirflexible structures allow them to be placed circumferentially around acurrent-carrying conductor, and may be used in limited-spaceapplications, to take current measurements of the current flow in suchconductors. A Rogowski coil generally consists of a helical coil of wirewith the lead from one end returning through the center of the coil tothe originating end such that both terminals are at the same end of thecoil. This configuration of a counter-wound Rogowski coil allows for itsuse on existing conductors arranged without access to thread the coil onthe conductor because one end is open. The Rogowski coil lacks an ironor other metal core, and thus does not suffer many of the disadvantagesof CTs. Many parameters may be adjusted to achieve desired results, suchas the winding density, the diameter of the coil, and the rigidity ofthe winding, to reduce sensitivity to external currents and magneticfields, and to reduce sensitivity to the positioning around theconductor whose current is to be measured.

The voltage induced in the coil is proportional to the rate of change ofcurrent in the conductor, and the output voltage of the Rogowski coil isconsiderably small, so the output is generally connected to anintegrator circuit to accurately integrate the signal to provide anoutput signal proportional to the current. Single-chip signal processorswith built-in analog to digital converters are often used for thispurpose.

As described in the art, for example by Power Electronic MeasurementsLtd of Nottingham UK (PEM) in technical notes for their Rogowskicoil-based products, Rogowski coils provide a variety of features makingthem useful for detecting variances in current, including: Widebandwidth, especially pertinent for power electronics; the ability tomeasure AC current in the presence of large DC current; non-saturationof the core, so measurements are highly linear; the ability to measurelarge current without risk of sustaining damage; minimal loadingeffects; flexibility and simplicity of installation in tight spaces;galvanically isolated analog input; and safety of operation.

Rogowski coils use a non-magnetic core to support the secondary winding.This arrangement yields only weak coupling between the primary andsecondary windings. As such, the outputs of Rogowski coils are mostlyunperturbed by the relative position of the primary conductor runningcoaxially within the coil. Furthermore, they are highly resistant toother nearby conductors carrying high currents because the mutualcoupling to the Rogowski coil's windings is constant. These coilsaccomplish these benefits through careful arrangements of the secondarywinding. The secondary winding has a constant cross-section, constantturn density, and a return wire that is maintained normal to the radialcross section of the winding. Rogowski coils are known in the art, forexample, in U.S. Pat. No. 9,588,147 describing such coils and electronicintegrator circuits for use therewith (see FIG. 1 thereof for a typicalillustration of a Rogowski coil current sensor with an integratedpreamplifier).

Using classical analysis, the output of the coil is a voltage V_(c)proportional to the rate of change of the encircled conductor's current,and is given by the time-scale derivative:

$\begin{matrix}{V_{c} = {\mu_{0}n{S\left( \frac{d{i_{p}(t)}}{dt} \right)}}} & (1)\end{matrix}$

where μ₀ is the magnetic constant (or permeability of vacuum), n is thespacing between the turns in the windings, S is the area of a crosssection of the core as defined by the coil's windings, and i_(p) is thecurrent in the conductor being measured.

An electronic integrator whose time constant is matched to the geometryof the coil is used to infer the encircled current. For example, apractical op-amp integrator with DC gain control known to those of skillin the art is illustrated in FIG. 1.

In an ideal operational amplifier, no current enters the input ports.Separate from magnetic and electric coupling, real operationalamplifiers generate internal noises (such as from resistors, currents,thermal noise KT/C, etc.), which are considered as uncorrelated externalsources at each input. The presence of input current noise implies thatthe feedback capacitor will saturate in the absence of a real inputsignal and produce a voltage drift at the output. To mitigate thisdrift, a resistor is added in parallel to discharge the capacitor at DC.Smaller resistors will discharge the capacitor quickly but they alsolower the cutoff frequency thereby reducing the bandwidth of theintegrator. A commonly used heuristic in electronic design is the “10×rule” which states that the feedback resistor must be 10 times largerthan the input resistor. This permits an acceptable compromise betweenlowering the DC gain while maintaining the bandwidth of the overallsensor. If a very large resistor is used instead, say 100 times larger,then the input current noise will be integrated and consequently thedrift will be larger.

There are known methods for performing electronic integration. Onecommon method involves the use of an integrator which is pre-cascaded bya high-pass filter. The difficulty in matching the time constants insuch solutions is described in the art, for example, by PEM. The art isin need of improved integrators for Rogowski coil and other currentsensors with advantages over, and without the disadvantages of,conventional designs.

SUMMARY OF THE INVENTION

Having observed the aforementioned problems with conventionalintegrators for Rogowski coils, the inventor hereof provides solutionsin the form of methods and devices to improve the performance of suchintegrators for current sensors by reducing drift while maintaining widebandwidth. In the present invention, field-effect transistors (FETs) areused to minimize the drift while simultaneously allowing for a verylarge feedback resistor. A junction-gate field-effect transistor (JFET)may be placed in parallel to the feedback resistor. By operating theJFET in the triode region, the net resistance in the feedback path canbe controlled electronically. Alternatively, a metal oxide field-effecttransistor (MOSFET) may be used, in which case the control signal iswell isolated from the resistor terminal. When the FET is conducting,the net feedback resistance is the parallel combination R_(f)∥R_(on).When the FET is open, the net feedback resistance is slightly largerthan R_(f).

The method and devices of the invention modify the feedback path of anintegrator in such a manner as to minimize drift in the output resultingfrom input current noise while simultaneously preserving the bandwidth.This configuration provides both automatic reset and gain control, byuse of FET networks which act as voltage controlled variable resistors.With this configuration, the integrator of the present invention reducesdrift because high frequencies having more negative voltage areinsufficient to close the FET, but low frequencies with less negativevoltage close the FET and bring it into the circuit. Thus, drift fromlow frequencies is effectively reduced while maintaining the widebandwidth of the integrator.

The invention described herein employs a method based on modulating thefeedback path of the integrator to adjust the gain on the output. Thegenerality of the input to such an integrator allows for it to be usednot only in current measurements but also in other fields in which driftshould be minimized while bandwidth is maintained, such as navigationand shock measurements. For example, accelerometer outputs can be doubleintegrated using the method of the invention to produce low driftposition estimates. The present invention is useful in a variety ofapplications, including diode pumped frequency discriminators;applications employing linearized JFETs in feedback paths; and practicalop-amp integrators.

In one aspect, the invention is directed to an integrator circuit foruse with current sensors, having an input for receiving an input signalfrom a current sensor; an op-amp receiving the input signal from theinput, the op-amp having an output providing an output voltage signal,the output voltage signal capable of being tapped for measurement; adiode pump comprising a first capacitor and a second capacitor, a loadresistor, a diode, a transistor, and a power source, the diode pumpreceiving the output voltage signal and providing a diode pump outputvoltage signal; a FET having a critical threshold voltage; and anintegrator resistor and an integrator capacitor in parallel. In thepresence of signal noise, the diode pump output voltage signal controlsthe FET to either close the gate when the diode pump output voltagesignal exceeds the critical threshold voltage or open the gate when thediode pump output voltage signal is less than the critical thresholdvoltage, such that the drift resulting from the signal noise isminimized while simultaneously maintaining the wide bandwidth of theintegrator. In another aspect, the FET is a JFET, or alternatively aMOSFET. In another aspect, the output voltage signal is tapped formeasurement by an external meter. In another aspect the diode pump maybe constructed on a single chip such that all the components of thediode pump are situate on a single module. In yet another aspect, thecurrent sensor is a Rogowski coil.

These and other aspects of the invention will be readily appreciated bythose of skill in the art from the description of the invention herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an embodiment of a practical integrator known in the artfor use with Rogowski coils.

FIG. 2 depicts an embodiment of the invention, illustrating anintegrator as a practical operational amplifier with frequency dependentgain control and automatic reset, allowing the feedback to drive thegate voltage of the FET via a frequency discriminator.

DETAILED DESCRIPTION OF THE INVENTION

With reference to the Figures, FIG. 1 illustrates a typical integratorknown in the art, in which the incoming current i₁ is passed to anop-amp, resistors and a capacitor, and emerges as output signal V_(o)providing the measurement of the incoming current. Such an integrator isprone to drift from high and low frequency noise, and while the choiceof resistors may be able to reduce such drift, it can do so effectivelyonly at the cost of a reduction of bandwidth. With lower values for theresistor R_(F), the capacitor C_(F) is discharged quickly and drift isreduced, but the cutoff frequency is concomitantly lowered, therebyreducing the effective bandwidth of the integrator. With higher valuesfor the resistor R_(F), the capacitor C_(F) is discharged less rapidly,maintaining bandwidth, but the input current noise will be integrated,thereby resulting in larger drift.

The invention described herein provides a feedback loop capable ofreducing drift and maintaining bandwidth by using a FET in the circuitwhich acts as a voltage controlled variable resistor. In a typicaln-type JFET, a negative voltage from gate to source V_(gs) increases thedepletion region. As V_(gs) becomes more negative it decreases thechannel width. The current going from drain to source I_(ds) depends onthe channel resistance drain to source r_(ds). When the depletion regionwidens and the channel narrows, the channel resistance r_(ds) increasesuntil the channel is depleted of all charge carriers and no currentflows. The particular V_(gs) where this occurs is known as the pinch offvoltage V_(c). When the voltage drain to source V_(ds) increases, V_(gs)remains constant while the reverse bias voltage of each pn junction willincrease as we move up the channel. The depletion region assumes atapered shape and the channel becomes pinched off at the drain end. Themaximum current at the drain I_(d) occurs when V_(gs)=0 and is definedas current drain to source shorted (or saturated), or I_(dss). When theJFET is biased with a large V_(ds) and V_(c)<V_(gs)<0, it will operatein the active region (or the saturation) region.

In the JFET linear region, (also known as the ohmic region or the trioderegion), the drain current is expressed as

$\begin{matrix}{I_{d} = {{V_{ds}\left( \frac{2I_{dss}}{V_{c}^{2}} \right)}\left( {V_{gs} - V_{c} - \frac{V_{ds}}{2}} \right)}} & (2)\end{matrix}$

When V_(ds)<<2 (V_(gs)−V_(c)), i.e., when the FET is operating in thelinear region,

$\begin{matrix}{I_{d} \approx {{V_{ds}\left( \frac{2I_{dss}}{V_{c}^{2}} \right)}\left( {V_{gs} - V_{c}} \right)}} & (3)\end{matrix}$

By definition, the channel resistance r_(ds) is

$\begin{matrix}{r_{ds} = {\frac{V_{ds}}{I_{d}}{{{{Vds}\mspace{14mu}{small}} = \left\lbrack {\left( \frac{2I_{dss}}{V_{c}^{2}} \right)\left( {V_{gs} - V_{c}} \right)} \right\rbrack^{- 1}}}}} & (4)\end{matrix}$

With the properties of such a FET, an improved integrator may beconstructed. In FIG. 2, an integrator (1) of the invention isillustrated. The coil voltage V_(in) (2) is the input of the operationalamplifier and it is a relatively weak signal. After passing throughresistor R₁ (3) the signal passes to op-amp (4). Rather than using theinput signal to control the integrator, as is done in conventionalintegrators, the invention uses the output V_(out) (15) of theoperational amplifier to automatically control the gain of theintegrator (1), and in the extreme case of DC input signals, to resetthe integrator (1).

This control is accomplished by means of a frequency to voltageconverter. In some embodiments, the converter is a diode pump comprisingcapacitors C₁ (5) and C₂ (6), resistor R (7), diode D₁ (9), transistorT₁ (10), and a power source (11). The first negative swing at the outputV_(out) (15) charges C₁ (5) through the base-emitter diode of T₁ (10) toV_(out) (15), and the subsequent positive swing to zero causes C₁ (5) todischarge into C₂ (6) so that

$\begin{matrix}{V_{p} = {V_{out}\left( \frac{C_{1}}{C_{1} + C_{2}} \right)}} & (5)\end{matrix}$

where V_(p) (8) is the diode pump output signal. The second negativeswing of V_(out) (15) charges C₁ (5) to (V_(p)+V_(out)) volts becausethe right hand connection of C₁ (5) is caught at V_(p) (8) by T₁ (10).When V_(out) (15) starts to return to ground for the second time D₁ (9)conducts immediately, in contrast to the situation in which V_(out) (15)must rise by

$V_{out}\left( \frac{C_{1}}{C_{1} + C_{2}} \right)$before D₁ (9) would conduct. The full rise of V_(out) (15) is thereforeshared by C₁ (5) and C₂ (6) as on the first positive swing, and theoutput therefore rises, as before by

${V_{out}\left( \frac{C_{1}}{C_{1} + C_{2}} \right)}.$This process is repeated so V_(p) (8) is a staircase function whosesteps are given by

${V_{out}\left( \frac{C_{1}}{C_{1} + C_{2}} \right)}.$The addition of the load resistor R (7) in parallel to the large C₂ (6)results in equal increments of charge transfer per cycle and the pumpacts as a frequency discriminator. The components of the diode pump areselected so that at DC (or an appropriately chosen low frequency limit)V_(p) (8) reaches the critical threshold (V_(c)) of the FET, which thenbegins to conduct. This will result in integrator capacitor C_(f) (14)discharging much more quickly than it would in the conventionalintegrator depicted in FIG. 1. When V_(p) (8) is less than V_(c), theFET is open, the net impedance of the feedback path is slightly smallerthan integrator resistor R_(f) (13). The resulting signal present atV_(out) (15) may be tapped for reading by a meter in addition to itbeing used to control the gain of the integrator (1). Configured in thismanner, the integrator maintains a large bandwidth while minimizing DCdrift.

In some embodiments, the diode pump may be constructed on a single chipsuch that all the components of the diode pump are situate on a singlemodule. In other embodiments, the frequency-to-voltage converter may bea chip such as an LM331 converter, in which case a p type FET (such as ap type JFET) would be used in place of an n type FET.

Those of skill in the art will readily appreciate that the components ofthe integrator and diode pump may be chosen to achieve particularlydesired results in particular applications.

EXAMPLES

The following Examples serve to illustrate the present invention and arenot intended to limit its scope in any way.

Example 1—an Integrator for Use with Current Sensors

An integrator (1) for use with current sensors such as Rogowski coils isconstructed as follows. Resistors R₁ (3) are selected with resistance of10 kΩ ohms. Diode pump capacitor C₁ (5) is selected with capacitance of1 μF, and C₂ (6) with capacitance of 100 μF. Load resistor R (7) isselected with resistance of 10 kΩ ohms. Integrator resistor R_(f) (13)is selected with resistance of 100 kΩ ohms. Integrator capacitor C_(f)(5) is selected with capacitance of 100 nF. The power source (11) is setto −10V. Diode D₁ (9) is a 1N4148 standard silicon switching signaldiode. Transistor T₁ (10) is a 2N3906 standard PNP transistor. FET Q₁(12) is a JFET J310 standard N-channel JFET. The op-amp is selected fromstandard op-amps such as LM741 and LM324. When a signal from a currentsensor such as a Rogowski coil is connected at V_(in) (2) the integratorthus constructed provides at V_(out) (15) from the op-amp a signal whichmay be read by a meter, and which signal provides an accuratemeasurement of the current with reduced drift and wide bandwidth.

The present invention is not to be limited in scope by the specificembodiments described above, which are intended as illustrations ofaspects of the invention. Functionally equivalent methods and componentsare within the scope of the invention. Various modifications of theinvention, in addition to those shown and described herein, will bereadily apparent to those skilled in the art from the foregoingdescription. Such modifications are intended to fall within the scope ofthe appended claims. All cited documents are incorporated herein byreference.

What is claimed is:
 1. An integrator circuit for use with currentsensors, comprising: an input for receiving an input signal from acurrent sensor; an op-amp receiving the input signal from the input, theop-amp having an output providing an output voltage signal, the outputvoltage signal being capable of being tapped for measurement; a diodepump comprising a first capacitor and a second capacitor, a loadresistor, a diode, a transistor, and a power source, the diode pumpreceiving the output voltage signal and providing a diode pump outputvoltage signal; a FET having a critical threshold voltage; and anintegrator resistor and an integrator capacitor in parallel; wherein, inthe presence of a signal noise, the diode pump output voltage signalcontrols the FET to either close the gate when the diode pump outputvoltage signal exceeds the critical threshold voltage or open the gatewhen the diode pump output voltage signal is less than the criticalthreshold voltage, such that a drift resulting from the signal noise isminimized while simultaneously maintaining a bandwidth of theintegrator.
 2. The integrator circuit of claim 1, wherein the FET is aJFET.
 3. The integrator circuit of claim 1, wherein the FET is a MOSFET.4. The integrator circuit of claim 1, wherein the output voltage signalis tapped for measurement by an external meter.
 5. The integratorcircuit of claim 1, wherein the diode pump is constructed on a singlechip.
 6. The integrator circuit of claim 1, wherein the current sensoris a Rogowski coil.